Finite Group Databasebeta

← #29572687

Subgroups — #29572687

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839653C211yesmaximal, characteristic
2#21445799C211yesmaximal, characteristic, complemented
3C2×#16839485C212yesmaximal
4#21443661C212yesmaximal, complemented
5C61×#1797C211yesmaximal, characteristic, complemented
6C22×#11758196C411yescharacteristic
7C22×#11758198C411yescharacteristic
8C22×#11758198C411yescharacteristic
9C22×#11758198C2211yescharacteristic
10C2×C4⋊#92418—21no—
11C2×C22⋊#92418C2212yes—
12#16839653—21no—
13#16839653—21no—
14#16839653—21no—
15#16839653—21no—
16C2×#14519684C411yescharacteristic
17C2×#14519684C2211yescharacteristic
18#16839517—21no—
19#16839485—24no—
20C22×C42×C61C2211yescharacteristic
21C2×C4⋊C8×C61—21no—
22C2×C22⋊C8×C61C2212yes—
23C61×#336—21no—
24C24×D61C2×C411yescharacteristic
25C23×Dic61C2×C411yescharacteristic
26C23×Dic61C2×C411yescharacteristic
27C23×Dic61C2×C411yescharacteristic
28C22×#92418—22no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—42no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×#11758198—21no—
40C2×#11758198—42no—
41C2×#11758198—42no—
42C2×#11758198D412yes—
43C2×#11758198Q812yes—
44C4⋊#92418—42no—
45C22⋊#92418—22no—
46C22⋊#92418—22no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51C23×C4×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C22×C8×C61—22no—
55C2×C42×C61—42no—
56C2×C42×C61D411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61D411yescharacteristic
60C4⋊C8×C61—42no—
61C22⋊C8×C61—22no—
62C22⋊C8×C61—22no—
63C24×C61C22×C411yescharacteristic
64C23×D61—21no—
65C23×D61—21no—
66C23×D61—22no—
67C23×D61—22no—
68C23×D61—41no—
69C23×D61—41no—
70C23×D61—41no—
71C23×D61—41no—
72C23×D61C4⋊C412yes—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C22⋊C411yescharacteristic
82C22×C4×C61C22⋊C411yescharacteristic
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×Q811yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×Dic61—21no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—22no—
96C22×Dic61—22no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61C4⋊C412yes—
104C2×C8×C61—42no—
105C2×C8×C61—42no—
106C2×C8×C61—42no—
107C42×C61—22no—
108C42×C61—22no—
109C42×C61—41no—
110C42×C61—41no—
111#11758198—22no—
112#11758198—22no—
113#11758198—22no—
114#11758198—22no—
115#11758198—42no—
116#11758198—42no—
117#11758198—42no—
118#11758198—42no—
119#11758196—42no—
120#11758196—42no—
121C2×#92418—42no—
122C2×#92418—42no—
123C2×#92418—42no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—21no—
128C23×C61C2×C22⋊C411yescharacteristic
129C23×C61C2×C4⋊C411yescharacteristic
130C23×C61#11711yescharacteristic
131C23×C61#13112yes—
132C23×C61#13112yes—
133C22×D61—22no—
134C22×D61—24no—
135C22×D61—42no—
136C22×D61—42no—
137C22×D61—41no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—42no—
144C22×D61—42no—
145C22×D61—42no—
146C22×D61—82no—
147C22×D61—82no—
148C22×D61—82no—
149C22×D61—82no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—44no—
169C2×C4×C61—44no—
170C2×C4×C61#9912yes—
171C2×C4×C61#10012yes—
172C2×C4×C61#12111yescharacteristic
173C2×C4×C61#12111yescharacteristic
174C2×C4×C61C22⋊Q811yescharacteristic
175C2×C4×C61C22⋊Q811yescharacteristic
176C2×Dic61—22no—
177C2×Dic61—42no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—42no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—82no—
188C2×Dic61—82no—
189C8×C61—82no—
190#92418—82no—
191#8561—611nomaximal, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—21no—
195C22×C61—21no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—22no—
199C22×C61—22no—
200C22×C61#38011yescharacteristic
201C22×C61#40811yescharacteristic
202C22×C61#40811yescharacteristic
203C22×C61C2×#9911yescharacteristic
204C22×C61#41011yescharacteristic
205C22×C61C2×#10011yescharacteristic
206C22×C61#41311yescharacteristic
207C22×C61#42412yes—
208C22×C61#43312yes—
209C2×D61—42no—
210C2×D61—42no—
211C2×D61—42no—
212C2×D61—84no—
213C2×D61—81no—
214C2×D61—81no—
215C2×D61—81no—
216C2×D61—81no—
217C2×D61—84no—
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—22no—
223C4×C61—22no—
224C4×C61—41no—
225C4×C61—41no—
226Dic61—42no—
227Dic61—81no—
228Dic61—81no—
229C2×#388—611no—
230#1797—611no—
231#1797D6111yescharacteristic, complemented
232C2×#323—612no—
233#1280—612no—
234C2×C61—22no—
235C2×C61—22no—
236C2×C61#146811yescharacteristic
237C2×C61#146911yescharacteristic
238C2×C61#147111yescharacteristic
239C2×C61#147311yescharacteristic
240C2×C61#179811yescharacteristic
241C2×C61#179911yescharacteristic
242C2×C61#180011yescharacteristic
243D61—82no—
244C22×C4⋊C4—611no—
245C22×C22⋊C4—611no—
246C22×C22⋊C4—611no—
247C22×C22⋊C4—611no—
248C22×C42C2×D6111yescharacteristic
249C2×C4⋊C8—21no—
250C2×C4⋊C8—1221no—
251C2×C22⋊C8—612no—
252C2×C22⋊C8C2×D6112yes—
253#388—1221no—
254#388—1221no—
255#388—1221no—
256#388—1221no—
257C2×#95—611no—
258C2×#95—611no—
259#336—21no—
260#336—1221no—
261#323—1224no—
262C61#856111yescharacteristic, complemented, Sylow
263C25—611no—
264C23×C4—611no—
265C23×C4—611no—
266C23×C4—611no—
267C23×C4C4×D6111yescharacteristic
268C23×C4C4×D6111yescharacteristic
269C23×C4C22×D6111yescharacteristic
270C22×C8—22no—
271C22×C8—1222no—
272C2×C4⋊C4—1221no—
273C2×C4⋊C4—1221no—
274C2×C4⋊C4—2442no—
275C2×C22⋊C4—612no—
276C2×C22⋊C4—612no—
277C2×C22⋊C4—1221no—
278C2×C22⋊C4—1221no—
279C2×C22⋊C4—1221no—
280C2×C22⋊C4—1221no—
281C2×C22⋊C4—1221no—
282C2×C22⋊C4—1221no—
283C2×C22⋊C4—1221no—
284C2×C22⋊C4—1221no—
285C2×C22⋊C4—2442no—
286C2×C22⋊C4—2442no—
287C2×C42—42no—
288C2×C42D24411yescharacteristic
289C2×C42D24411yescharacteristic
290C2×C42C22⋊D6111yescharacteristic
291C2×C42C22⋊D6111yescharacteristic
292C4⋊C8—42no—
293C4⋊C8—2442no—
294C22⋊C8—22no—
295C22⋊C8—22no—
296C22⋊C8—1222no—
297C22⋊C8—1222no—
298#95—1221no—
299#95—1221no—
300#95—1221no—
301#95—1221no—
302C24—612no—
303C24—1222no—
304C24—1222no—
305C24—1221no—
306C24—1221no—
307C24—2441no—
308C24—2441no—
309C24—2441no—
310C24—2441no—
311C24C2×C4×D6111yescharacteristic
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—612no—
321C22×C4—1221no—
322C22×C4—1221no—
323C22×C4—1222no—
324C22×C4—1222no—
325C22×C4—1221no—
326C22×C4—1221no—
327C22×C4—2441no—
328C22×C4—2441no—
329C22×C4—2441no—
330C22×C4—2441no—
331C22×C4—2441no—
332C22×C4—2441no—
333C22×C4#1175819811yescharacteristic
334C22×C4#1175819811yescharacteristic
335C22×C4#1175819811yescharacteristic
336C22×C4#1175819811yescharacteristic
337C22×C4C2×D24411yescharacteristic
338C22×C4D4×D6111yescharacteristic
339C22×C4#1175822411yescharacteristic
340C22×C4Q8×D6111yescharacteristic
341C22×C4#1175822611yescharacteristic
342C22×C4C2×C22⋊D6111yescharacteristic
343C2×C8—42no—
344C2×C8—42no—
345C2×C8—42no—
346C2×C8—2442no—
347C2×C8—2442no—
348C2×C8—2442no—
349C4⋊C4—2442no—
350C4⋊C4—2442no—
351C22⋊C4—1222no—
352C22⋊C4—1222no—
353C22⋊C4—1222no—
354C22⋊C4—1222no—
355C22⋊C4—2442no—
356C22⋊C4—2442no—
357C22⋊C4—2442no—
358C22⋊C4—2442no—
359C42—22no—
360C42—22no—
361C42—41no—
362C42—41no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—1224no—
368C23—1222no—
369C23—4882no—
370C23—4882no—
371C23—4882no—
372C23—4882no—
373C23—2442no—
374C23—2442no—
375C23—2442no—
376C23—2442no—
377C23—2441no—
378C23—2441no—
379C23—2441no—
380C23—2441no—
381C23—2441no—
382C23—2441no—
383C23—2442no—
384C23C2×#1175819811yescharacteristic
385C23C4⋊C4×D6111yescharacteristic
386C23#1451973511yescharacteristic
387C23#1451978312yes—
388C23#1451978512yes—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—1222no—
410C2×C4—4882no—
411C2×C4—4882no—
412C2×C4—2441no—
413C2×C4—2441no—
414C2×C4—2441no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2442no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2442no—
422C2×C4#1451969112yes—
423C2×C4#1451969312yes—
424C2×C4#1451974811yescharacteristic
425C2×C4#1451975211yescharacteristic
426C2×C4#1451975311yescharacteristic
427C2×C4#1451975711yescharacteristic
428C8—82no—
429C8—4882no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—4884no—
439C22—4884no—
440C22—4881no—
441C22—4881no—
442C22—4881no—
443C22—4881no—
444C22—2442no—
445C22—2442no—
446C22—2442no—
447C22#1683961911yescharacteristic
448C22#1683972811yescharacteristic
449C22#1683973011yescharacteristic
450C22C2×#1451969111yescharacteristic
451C22#1683973511yescharacteristic
452C22C2×#1451969311yescharacteristic
453C22#1683974411yescharacteristic
454C22#1683978712yes—
455C22#1683982212yes—
456C4—22no—
457C4—22no—
458C4—21no—
459C4—21no—
460C4—21no—
461C4—21no—
462C4—41no—
463C4—41no—
464C4—4881no—
465C4—4881no—
466C4—2442no—
467C2—22no—
468C2—22no—
469C2—4882no—
470C2#2144416811yescharacteristic
471C2#2144417211yescharacteristic
472C2#2144417811yescharacteristic
473C2#2144418611yescharacteristic
474C2#2144580011yescharacteristic
475C2#2144580411yescharacteristic
476C2#2144580811yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC24×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1797C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61C2×C4
cosocleC23×C4×C61C23
hypercenter#1797D61
hypocenterC61#8561
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21445799C2semidirect
4. #21443661C2semidirect
5. C61×#1797C2semidirect
231. #1797D61semidirect
262. C61#8561semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168396532
#214457992
C2×#168394852
#214436612
C61×#17972
#856161